Falmouth voters strongly supported a referendum question Tuesday authorizing town officials to borrow as much as $2.8 million to help renovate and expand the Falmouth Memorial Library.

The vote was 4,005 to 2,559 for a bond that would cover half of the project’s estimated $5.6 million cost. The library association is expected to raise the balance.

The project would fix a variety of problems with the existing library, including a leaky basement, a failing roof and an outdated sprinkler system. It also would add 6,000 square feet of space, expand collection areas by 30 percent, improve web access and increase parking.